The Ljung-Box modified $Q^*$ statistic has an asymptotic chi-square distribution with $m$ degrees of freedom and can be used to test the null hypothesis that the time series is not serially correlated.$$Q^*(m) \sim \chi_{\nu=m}^2()$$Where:

$\chi_{\nu}^2()$ is the Chi-square probability distribution function.

$\nu$ is the degrees of freedom for the Chi-square distribution.

The Ljung-Box test is a suitable test for all sample sizes including small ones.

This is one-side (i.e. one-tail) test, so the computed p-value should be compared with the whole significance level ($\alpha$).